Traveling wave solutions in a two-group SIR epidemic model with constant recruitment
Traveling wave solutions in a two-group SIR epidemic model with constant recruitment
复制标题
DOI：
10.1007/s00285-018-1227-9
复制
发表时间：
2018-03
影响因子：
1.9
通讯作者：
Lin Zhao;Zhi-Cheng Wang;S. Ruan
中科院分区：
文献类型：
--
作者：
Lin Zhao;Zhi-Cheng Wang;S. Ruan
宿主异质性可以通过使用群体中的多组结构来建模。本文研究了一类具有时滞和常数补充的两组SIR传染病模型行波解的存在性和不存在性，证明了行波解的存在性由基本再生数决定。我们证明（i）当基本再生数存在时，存在一个最小波速，使得对于每一个，系统都存在一个非平凡的行波解，无非平凡行波满足系统;（ii）当系统不存在非平凡行波时。最后，我们给出了一些数值模拟，以显示存在的行波系统。
Host heterogeneity can be modeled by using multi-group structures in the population. In this paper we investigate the existence and nonexistence of traveling waves of a two-group SIR epidemic model with time delay and constant recruitment and show that the existence of traveling waves is determined by the basic reproduction numberMore specifically, we prove that (i) when the basic reproduction numberthere exists a minimal wave speedsuch that for eachthe system admits a nontrivial traveling wave solution with wave speedcand forthere exists no nontrivial traveling wave satisfying the system; (ii) whenthe system admits no nontrivial traveling waves. Finally, we present some numerical simulations to show the existence of traveling waves of the system.